A significant improvement over the standard MRT-LB methods based on raw moments is to consider performing relaxation of central moments to their equilibria under collision [1]}. Here, the central moments are obtained from the distribution functions based on the peculiar velocity and naturally preserves the Galilean invariance of all the moments independently supported by the lattice. The central moment equilibria are generally constructed via a matching principle based on the continuous Maxwell distribution function. As a result, when compared to the standard SRT-LB and MRT-LB schemes, whose equilibria generally involve fluid velocity terms truncated up to the second order, the central moment LB methods involve higher order fluid velocity terms, which support their enhanced stability characteristics. As discussed in Ref. [2]}, the method can be constructed using different moment basis, including those based on non-orthogonal moments. Recently, the central moment LB method has been further extended, improved and applied to variety of flowing systems (see e.g., [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}). Moreover, the numerical investigations in Refs. [6]}, [7]}, [13]}, [19]} demonstrated the superior stability characteristics of the central moment LB schemes. It should, however, be mentioned here that the central moment LBM has so far been developed only for square lattice grids in 2D and cubic lattice grids in 3D.
